伽马分布独立随机变量加权和的尾概率界

Tail Probability Bound of Weighted Sum of Independent Random Variables of Gamma Distribution

研究了单、双边伽马分布独立随机变量加权和的尾概率界。利用服从伽马分布的独立随机变量加权后的期望和概率母函数,对服从伽马分布的尾概率进行单边估计,从而得到一个独立随机变量加权和的尾概率界,并且利用CHEBYSHEV不等式和高斯尾部估计方法,给出了双边伽马分布独立随机变量加权和的尾概率界。

The tail probability bound of the weighted sum of independent random variables of single and bilateral gamma distributions is studied.The tail probability bound of weighted sum of independent random variables of gamma distributions is estimated unilaterally by using the weighted expectation and probability generating function of independent random variables subject to gamma distributions,and a tail probability bound of weighted sum of independent random variables is obtained by CHEBYSHEV inequality and Gaussian tail estimation method.The tail probability bound of weighted sum of independent random variables of bilateral gamma distribution is given.